You didn't say anything about the ignition key. This is how the buzzer is supposed to work, when the key is in the ignition and the driver's door is open. If it's doing this any time the driver's door is open, regardless of the key being in the ignition, then it's likely the switch in the ignition cylinder is broken or shorted. If you don't care about making the buzzer work properly and just want it to stop completely, you could either disconnect the buzzer, or there might be an individual fuse for this that you could pull, although this is an awful small load, so it's probably fused through some other circuit.